Massive partition functions and complex eigenvalue correlations in Matrix Models with symplectic symmetry

Details Massive partition functions and complex eigenvalue correlations in Matrix Models with symplectic symmetry Massive partition functions and complex eigenvalue correlations in Matrix Models with symplectic symmetry

2006-06-23

arxiv.org/abs/math-ph/0606060v2

Nucl.Phys.B766:150-177,2007

Physics

Mathematical Physics

24 pages, v2 published version: discussion + refs added, typos corected

Scientific paper

10.1016/j.nuclphysb.2006.12.008

We compute all massive partition functions or characteristic polynomials and their complex eigenvalue correlation functions for non-Hermitean extensions of the symplectic and chiral symplectic ensemble of random matrices. Our results are valid for general weight functions without degeneracies of the mass parameters. The expressions we derive are given in terms of the Pfaffian of skew orthogonal polynomials in the complex plane and their kernel. They are much simpler than the corresponding expressions for symplectic matrix models with real eigenvalues, and we explicitly show how to recover these in the Hermitean limit. This explains the appearance of three different kernels as quaternion matrix elements there in terms of derivatives of a single kernel here. We compare to the Hermitean limit of complex matrix models with unitary symmetry leading to some determinantal identities.

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